Browsing Faculty Works, Department of Mathematics by Title
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H2QUASIOPTIMAL MODEL ORDER REDUCTION FOR QUADRATICBILINEAR CONTROL SYSTEMS
We investigate the optimal model reduction problem for largescale quadraticbilinear (QB) control systems. Our contributions are threefold. First, we discuss the variational analysis and the Volterra series formulation ... 
How soap bubbles freeze
(Springer Nature, 20190618)Droplets or puddles tend to freeze from the propagation of a single freeze front. In contrast, videographers have shown that as soap bubbles freeze, a plethora of growing ice crystals can swirl around in a beautiful effect ... 
Improved scaling for quantum monte carlo on insulators
(Siam Publications, 2011)Quantum Monte Carlo (QMC) methods are often used to calculate properties of many body quantum systems. The main cost of many QMC methods, for example, the variational Monte Carlo (VMC) method, is in constructing a sequence ... 
Individual and situational factors related to undergraduate mathematics instruction
(20190628)Abstract Background In the US, there is significant interest from policy boards and funding agencies to change students’ experiences in undergraduate mathematics classes. Even ... 
inertiainduced breakup of highly viscous drops subjected to simple shear
(AIP Publishing, 200305)We investigate the inertiadriven breakup of viscous drops suspended in a less viscous liquid under simple shear. For Stokes flow, it is known that there is a critical value of the viscosity ratio, beyond which breakup ... 
Inexact solves in interpolatory model reduction
(Elsevier Science Inc, 20120415) 
Integral equation methods for the inverse problem with discontinuous wave speed
(AIP Publishing, 199607)The recovery of the coefficient H(x) in the onedimensional generalized Schrodinger equation d(2) psi dx(2)+k(2)H(x)(2) psi=Q(x)psi, where H(x) is a positive, piecewise continuous function with positive limits H+/ as ... 
interaction function and lattice duals
(AIP Publishing, 197710)An interaction function is defined for lattice models in statistical mechanics. A correlation function expansion is derived, giving a direct proof of the duality relations for correlation functions. 
internal capillarygravity waves of a twolayer fluid with free surface over an obstruction  Forced extended KdV equation
(AIP Publishing, 199602)In this paper we study steady capillarygravity waves in a twolayer fluid bounded above by a free surface and below by a horizontal rigid boundary with a small obstruction. Two critical speeds for the waves are obtained. ... 
Interpolatory Hinfinity model reduction
(Elsevier Science Bv, 20130701) 
Interpolatory methods for $\mathcal{H}_\infty$ model reduction of multiinput/multioutput systems
(Springer, 20160801)We develop here a computationally effective approach for producing highquality $\mathcal{H}_\infty$approximations to large scale linear dynamical systems having multiple inputs and multiple outputs (MIMO). We extend an ... 
Interpolatory Model Reduction of Parameterized Bilinear Dynamical Systems
Interpolatory projection methods for model reduction of nonparametric linear dynamical systems have been successfully extended to nonparametric bilinear dynamical systems. However, this is not the case for parametric ... 
Interpolatory projection methods for parameterized model reduction
(Siam Publications, 2011)We provide a unifying projectionbased framework for structurepreserving interpolatory model reduction of parameterized linear dynamical systems, i.e., systems having a structured dependence on parameters that we wish to ... 
Interpolatory weightedH2 model reduction
(PergamonElsevier Science Ltd, 20130501) 
An introduction to compartmental modeling for the budding infectious disease modeler
(Taylor & Francis, 20180816)Mathematical models are ubiquitous in the study of the transmission dynamics of infectious diseases, In particular, the classic ‘susceptibleinfectiousrecovered’ (SIR) paradigm provides a modeling framework that can be ... 
Invariant measures for the tochastic von Karman plate equation
(Siam Publications, 2005)We prove the existence of an invariant measure for the von Karman plate equation with random noise. The nonlinear term which symbolizes the von Karman equation inhibits the standard procedure for the existence of an invariant ... 
inverse scattering in 1D nonhomogeneous media and recovery of the wave speed
(AIP Publishing, 199204)The inverse scattering problem for the 1D Schrodinger equation d2psi/dx2 + k2psi = k2P(x)psi + Q(x)psi is studied. This equation is equivalent to the 1D wave equation with speed 1/ squareroot 1  P(x) in a nonhomogeneous ... 
Inverse scattering on the line for a Dirac system
(AIP Publishing, 199111)The wholeline version of the GelfandLevitanMarchenko (GLM) equation for a Dirac system is studied. A new derivation of the GLM equation is given, under weaker hypotheses than Frolov's earlier treatment [Sov. Math. Dok1. ... 
inverse wave scattering with discontinuous wave speed
(AIP Publishing, 199506)The inverse scattering problem on the line is studied for the generalized Schrödinger equation (d 2ψ/dx 2)+k 2 H(x)2ψ=Q(x)ψ, where H(x) is a positive, piecewise continuous function with positive limits H ± as x → ±∞. This ... 
JigCell Run Manager (JCRM): a tool for managing large sets of biochemical model parametrizations
(Biomed Central Ltd, 20151224)Background Most biomolecular reaction modeling tools allow users to build models with a single list of parameter values. However, a common scenario involves different parameterizations of the model to account for the ...